论文标题
重力子系统的Metripercic几何形状
Metriplectic geometry for gravitational subsystems
论文作者
论文摘要
总体而言，很难将可观察到的物质定位，例如能量，角动量或质量中心。困难是存在耗散。一个自身将其重力限制在有限区域的自我磨损系统，将一些指控辐射到环境中。在正式的层面上，耗散意味着某些差异性不是哈密顿人。实际上，在相空间上没有哈密顿人可以将区域相对于田地移动。最近，引入了协变量空间的扩展以解决该问题。在扩展的相空间上，科马尔的指控是哈密顿量。它们是穿着差异的发电机。虽然构造是合理的，但物理意义尚不清楚。在制定一种以新颖方式考虑耗散的几何方法之前，我们会提供重要的审查。我们的方法基于Metripercic几何形状，这是一种用于耗散系统描述的框架。我们引入了一个leibniz支架，而不是泊松支架，这是一个偏斜的对称和对称支架的总和。对称项是由于辐射引起的电荷损失。在Metripercoric空间上，指控是哈密顿尔顿人，但在自己的流程中并没有保守。
In general relativity, it is difficult to localise observables such as energy, angular momentum, or centre of mass in a bounded region. The difficulty is that there is dissipation. A self-gravitating system, confined by its own gravity to a bounded region, radiates some of the charges away into the environment. At a formal level, dissipation implies that some diffeomorphisms are not Hamiltonian. In fact, there is no Hamiltonian on phase space that would move the region relative to the fields. Recently, an extension of the covariant phase space has been introduced to resolve the issue. On the extended phase space, the Komar charges are Hamiltonian. They are generators of dressed diffeomorphisms. While the construction is sound, the physical significance is unclear. We provide a critical review before developing a geometric approach that takes into account dissipation in a novel way. Our approach is based on metriplectic geometry, a framework used in the description of dissipative systems. Instead of the Poisson bracket, we introduce a Leibniz bracket - a sum of a skew-symmetric and a symmetric bracket. The symmetric term accounts for the loss of charge due to radiation. On the metriplectic space, the charges are Hamiltonian, yet they are not conserved under their own flow.
